Generating functions and multiplicity formulas: The case of rank two simple Lie algebras

Abstract

A procedure is described that makes use of the generating function of characters to obtain a new generating function H giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from H explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown.PACS: 02.20.Qs, 02.30.Ik, 03.65.Fd.

On the generating function of weight multiplicities for the representations of the Lie algebra C2

“…As a matter of fact, we have recently computed the H(t i ; y j ) generating functions for all rank-two simple Lie algebras and used them to extract explicit formulas for the multiplicities of some specific weights in all representations. 20 We think that the same approach can be applied to obtain similar results for other Lie algebras of higher rank.…”

Multiplicity formulas for fundamental strings of representations of classical Lie algebras

“…In order to end the description of previous results in this large area we name a few recent related results, though the list is far from being complete: [Co05], [BBCV06], [Bl08], [Sc12], [Ma14], [FGP14], [FGP15a], [FGP15b], [FGP17], [Ca17].…”